// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "main.h"
#include <Eigen/Eigenvalues>
#include <Eigen/LU>
#include <limits>

template<typename MatrixType>
bool
find_pivot(typename MatrixType::Scalar tol, MatrixType& diffs, Index col = 0)
{
	bool match = diffs.diagonal().sum() <= tol;
	if (match || col == diffs.cols()) {
		return match;
	} else {
		Index n = diffs.cols();
		std::vector<std::pair<Index, Index>> transpositions;
		for (Index i = col; i < n; ++i) {
			Index best_index(0);
			if (diffs.col(col).segment(col, n - i).minCoeff(&best_index) > tol)
				break;

			best_index += col;

			diffs.row(col).swap(diffs.row(best_index));
			if (find_pivot(tol, diffs, col + 1))
				return true;
			diffs.row(col).swap(diffs.row(best_index));

			// move current pivot to the end
			diffs.row(n - (i - col) - 1).swap(diffs.row(best_index));
			transpositions.push_back(std::pair<Index, Index>(n - (i - col) - 1, best_index));
		}
		// restore
		for (Index k = transpositions.size() - 1; k >= 0; --k)
			diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second));
	}
	return false;
}

/* Check that two column vectors are approximately equal up to permutations.
 * Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(),
 * however this strategy is numerically inacurate because of numerical cancellation issues.
 */
template<typename VectorType>
void
verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2)
{
	typedef typename VectorType::Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;

	VERIFY(vec1.cols() == 1);
	VERIFY(vec2.cols() == 1);
	VERIFY(vec1.rows() == vec2.rows());

	Index n = vec1.rows();
	RealScalar tol = test_precision<RealScalar>() * test_precision<RealScalar>() *
					 numext::maxi(vec1.squaredNorm(), vec2.squaredNorm());
	Matrix<RealScalar, Dynamic, Dynamic> diffs =
		(vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2();

	VERIFY(find_pivot(tol, diffs));
}

template<typename MatrixType>
void
eigensolver(const MatrixType& m)
{
	/* this test covers the following files:
	   ComplexEigenSolver.h, and indirectly ComplexSchur.h
	*/
	Index rows = m.rows();
	Index cols = m.cols();

	typedef typename MatrixType::Scalar Scalar;
	typedef typename NumTraits<Scalar>::Real RealScalar;

	MatrixType a = MatrixType::Random(rows, cols);
	MatrixType symmA = a.adjoint() * a;

	ComplexEigenSolver<MatrixType> ei0(symmA);
	VERIFY_IS_EQUAL(ei0.info(), Success);
	VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal());

	ComplexEigenSolver<MatrixType> ei1(a);
	VERIFY_IS_EQUAL(ei1.info(), Success);
	VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
	// Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus
	// another algorithm so results may differ slightly
	verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues());

	ComplexEigenSolver<MatrixType> ei2;
	ei2.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
	VERIFY_IS_EQUAL(ei2.info(), Success);
	VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
	VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
	if (rows > 2) {
		ei2.setMaxIterations(1).compute(a);
		VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
		VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
	}

	ComplexEigenSolver<MatrixType> eiNoEivecs(a, false);
	VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
	VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());

	// Regression test for issue #66
	MatrixType z = MatrixType::Zero(rows, cols);
	ComplexEigenSolver<MatrixType> eiz(z);
	VERIFY((eiz.eigenvalues().cwiseEqual(0)).all());

	MatrixType id = MatrixType::Identity(rows, cols);
	VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));

	if (rows > 1 && rows < 20) {
		// Test matrix with NaN
		a(0, 0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
		ComplexEigenSolver<MatrixType> eiNaN(a);
		VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
	}

	// regression test for bug 1098
	{
		ComplexEigenSolver<MatrixType> eig(a.adjoint() * a);
		eig.compute(a.adjoint() * a);
	}

	// regression test for bug 478
	{
		a.setZero();
		ComplexEigenSolver<MatrixType> ei3(a);
		VERIFY_IS_EQUAL(ei3.info(), Success);
		VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(), RealScalar(1));
		VERIFY((ei3.eigenvectors().transpose() * ei3.eigenvectors().transpose()).eval().isIdentity());
	}
}

template<typename MatrixType>
void
eigensolver_verify_assert(const MatrixType& m)
{
	ComplexEigenSolver<MatrixType> eig;
	VERIFY_RAISES_ASSERT(eig.eigenvectors());
	VERIFY_RAISES_ASSERT(eig.eigenvalues());

	MatrixType a = MatrixType::Random(m.rows(), m.cols());
	eig.compute(a, false);
	VERIFY_RAISES_ASSERT(eig.eigenvectors());
}

EIGEN_DECLARE_TEST(eigensolver_complex)
{
	int s = 0;
	for (int i = 0; i < g_repeat; i++) {
		CALL_SUBTEST_1(eigensolver(Matrix4cf()));
		s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4);
		CALL_SUBTEST_2(eigensolver(MatrixXcd(s, s)));
		CALL_SUBTEST_3(eigensolver(Matrix<std::complex<float>, 1, 1>()));
		CALL_SUBTEST_4(eigensolver(Matrix3f()));
		TEST_SET_BUT_UNUSED_VARIABLE(s)
	}
	CALL_SUBTEST_1(eigensolver_verify_assert(Matrix4cf()));
	s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4);
	CALL_SUBTEST_2(eigensolver_verify_assert(MatrixXcd(s, s)));
	CALL_SUBTEST_3(eigensolver_verify_assert(Matrix<std::complex<float>, 1, 1>()));
	CALL_SUBTEST_4(eigensolver_verify_assert(Matrix3f()));

	// Test problem size constructors
	CALL_SUBTEST_5(ComplexEigenSolver<MatrixXf> tmp(s));

	TEST_SET_BUT_UNUSED_VARIABLE(s)
}
